(4z+2)(9+z)=0

Solution for (4z+2)(9+z)=0 equation:

Simplifying
(4z + 2)(9 + z) = 0

Reorder the terms:
(2 + 4z)(9 + z) = 0

Multiply (2 + 4z) * (9 + z)
(2(9 + z) + 4z * (9 + z)) = 0
((9 * 2 + z * 2) + 4z * (9 + z)) = 0
((18 + 2z) + 4z * (9 + z)) = 0
(18 + 2z + (9 * 4z + z * 4z)) = 0
(18 + 2z + (36z + 4z2)) = 0

Combine like terms: 2z + 36z = 38z
(18 + 38z + 4z2) = 0

Solving
18 + 38z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 19z + 2z2) = 0

Factor a trinomial.
2((9 + z)(1 + 2z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve:

Simplifying
9 + z = 0

Solving
9 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + z = 0 + -9
z = 0 + -9

Combine like terms: 0 + -9 = -9
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(1 + 2z)' equal to zero and attempt to solve:

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-9, -0.5}